Question

cho: \(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\) ( với \(a,b,c\ne0;b\ne c\)) cmr: \(\frac{a}{c}=\frac{a-c}{c-b}\)

Answer 1

\(\frac{1}{c}=\frac{1}{2}(\frac{1}{a}+\frac{1}{b})\)

\(\Rightarrow\frac{1}{c}:\frac{1}{2}=\frac{1}{a}+\frac{1}{b}\)

\(\Rightarrow\frac{2}{c}=\frac{a}{ab}+\frac{b}{ab}\)

\(\Rightarrow\frac{2}{c}=\frac{a+b}{ab}\)

\(\Rightarrow2ab=(a+b)\cdot c\)

\(\Rightarrow ab+ab=ac+bc\)

\(\Rightarrow ab-bc=ac-ab\)

\(\Rightarrow b(a-c)=a(c-b)\)

\(\frac{a}{c}=\frac{a-c}{c-b}(đpcm)\)

Answer 2

\(\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{a}+\frac{1}{b}\right)\Rightarrow\frac{1}{c}=\frac{1}{2}.\left(\frac{a+b}{ab}\right)\Rightarrow\frac{1}{c}=\frac{a+b}{2ab}\)

\(\Rightarrow ac+cb=2ab\Rightarrow ac-ab=-cb+ba\Rightarrow a.\left(c-b\right)=b.\left(a-c\right)\)

\(\Rightarrow\frac{a}{b}=\frac{a-c}{c-b}\left(đpcm\right)\)

bn ghi sai đề kìa :v

Answer 3

mk ghi đúng mà

Answer 4

Bạn Tử Thần ơi sao \(b\left(a-c\right)=a\left(c-b\right)\) lại suy ra đc \(\frac{a}{c}=\frac{a-c}{c-b}\) được

Answer 5

Có \(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)\)

\(\Rightarrow\frac{2}{c}=\frac{1}{a}+\frac{1}{b}\)

\(\Rightarrow\frac{2}{c}=\frac{a+b}{ab}\)

\(\Rightarrow2ab=ca+cb\)

\(\Rightarrow ab-cb=ca-ab\)

\(\Rightarrow\left(a-c\right)b=a\left(c-b\right)\)

\(\Rightarrow\frac{a}{b}=\frac{a-c}{c-b}\)

Bạn ghi sai đề nha!!

Answer 6

ak đúng a/b chứ

Answer 7

\(\frac{a}{c}=\frac{a-c}{c-b}=\frac{a-a+c}{c-c+b}=\frac{c}{b}\Rightarrow c^2=ab\)(1)

\(\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{a}+\frac{1}{b}\right)=\frac{a+b}{2ab}=\frac{a+b}{c^2}\Rightarrow a+b=c\)(2)

mà (1) và (2)  \(\Rightarrow ab=\left(a+b\right)^2\Rightarrow ab=a^2+2ab+b^2\Rightarrow a^2+ab+b^2=0\Rightarrow a^2+b^2=-ab=-c^2\)

vô lí chưa :)

Answer 8

ngu như chó